Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-18T20:15:16.211Z Has data issue: false hasContentIssue false
  • English
  • Français

Distortion of certain Voronoi tesselations when one particle moves

Published online by Cambridge University Press:  14 July 2016

Luis-M. Cruz Orive
Luis-M. Cruz Orive*
Affiliation:
University of Bern
*
∗Postal address: Department of Anatomy, University of Bern, Bühlstrasse 26, CH-3000 Bern 9, Switzerland.
Get access Rights & Permissions [Opens in a new window]

Abstract

Some properties of the Voronoi polygon associated with a moving particle in a regular tessellation are studied. In particular, the area of the variable polygon has played a relevant role in previous studies on plant competition, animal predation, adjustment of the sex ratio in bisexual populations and the gregarious behaviour of animal species.

Keywords

GEOMETRICAL PROBABILITYVORONOI POLYGONSREGULAR TESSELLATIONSMOVING PARTICLESIDE NUMBERAREA
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 1 , March 1979 , pp. 95 - 103
Copyright
Copyright © Applied Probability Trust 1979 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Cannings, C. and Cruz Orive, L.-M. (1975) On the adjustment of the sex ratio and the gregarious behaviour of animal populations. J. Theoret. Biol. 55, 115–136.Google Scholar
Fischer, R. A. and Miles, R. E. (1973) The role of spatial pattern in the competition between crop plants and weeds. A theoretical analysis. Math. Biosci. 18, 335–350.Google Scholar
Halmos, P. R. (1974) Measure Theory. Springer–Verlag, New York.Google Scholar
Hamilton, W. D. (1971) Geometry for the selfish herd. J. Theoret. Biol. 31, 295–311.Google Scholar
Robbins, H. E. (1944) On the measure of a random set. Ann. Math. Statist. 15, 70–74.Google Scholar
Rogers, C. A. (1964) Packing and Covering. Cambridge University Press.Google Scholar